Having played in the Champions League at the best stadiums Europe has to offer, Cole is certain the Hammers' new ground will provide an equally-inspiring venue.
Cole told West Ham TV: "With all the things that happened there last summer, that's still firmly in people's minds. Now we want to put on great nights for the fans, European nights - that has to be the plan. You've got to look high, we want to play the top clubs in Europe, the Barcelonas, the Milans.
"That's the dream for everyone, the owners are West Ham people. They want it to happen, we want it to happen. The gaffer's done a great job, he's excited by it, so it's a great time and we want to bring some big nights there for the punters."